The party linked to Thailand's self-exiled former leader Thaksin Shinawatra says it had opened negotiations with other anti-junta parties to try to form a government.
The Pheu Thai party won 138 seats in the House of Representatives and the pro-army Palang Pracharat party won 96 seats, according to the Election Commission after the country's first vote since a 2014 coup.
But the winners of 150 of the lower house seats are still unclear, and the overall winner of Sunday's election may not emerge for weeks.
The commission has said it will announce the official results of the final 150 seats in the 500-seat parliament on May 9.
Pheu Thai secretary-general Phumtham Wechayachai said the votes cast for anti-junta parties showed a desire to return to democratic rule and that must be respected.
"From today, we will start negotiating with other parties (to form a government)," he told the news conference.
Thailand's pro-army Palang Pracharat party said on Monday it aims to form a government after winning the most votes in the country's first election since a 2014 coup.
"Palang Pracharat will talk to like-minded parties who share the same ideology and standpoint to move the country forward, which will take a while," Kobsak said.
Many Thais took to social media to voice their suspicions about the results of an election that critics had said was systematically skewed in favour of the military from the outset.
Thai-language hashtags that translated as "Election Commission screw-up" and "cheating the election" were trending on Twitter in Thailand.
Many tweets referred to inconsistencies between the numbers for voter turnout and ballots cast in some parliamentary constituencies.
Some questioned the overall turnout of less than 70 per cent, which was much lower than expected.
Australian Associated Press